The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠i = ∠j, ∠g is twice ∠j, ∠h is twice ∠k and ∠i is less than ∠k by 27°.
- Find ∠i.
- Find the difference between ∠g and ∠i.
(a)
∠i = 1 u
∠j = 1 u
∠k = 1 u + 27°
1 u + 27° + 1 u + 27° + 1 u = 180° (Angles sum of triangle)
3 u + 54° = 180°
3 u = 180° - 54° = 126°
1 u = 126° ÷ 3 = 42°
∠i = 1 u = 42°
(b)
∠g = 2 u
∠g - ∠i
= 2 u - 1 u
= 1 u
= 1 x 42°
= 42°
Answer(s): (a) 42°; (b) 42°